Low-frequency Limit Research Articles

Anomalous dispersion of Lamb waves in Ge cubic crystal

The current research is concerned with the study of Lamb waves propagating in a traction-free Ge plate with its basal (0,0,1) plane coinciding with the median plane of the plate. The analysis reveals (i) additional dispersion modes stepping down below the lowest cutoff frequency and resembling the (quasi) symmetric fundamental mode; (ii) the additional low-frequency limits; and (iii) multiple crossing points at the intersections of the transonic Rayleigh branch with the higher Lamb modes. The observed phenomena indicate a substantial difference in dispersion properties of Lamb waves in Ge plates compared to those of isotropic plates, namely additional low-frequency limits, multiple crossing points, and the additional fundamental branch.

Control of the Geometric Phase and Nonequivalence between Geometric-Phase Definitions in the Adiabatic Limit.

If the time evolution of a quantum state leads back to the initial state, a geometric phase is accumulated that is known as the Berry phase for adiabatic evolution or as the Aharonov-Anandan (AA) phase for nonadiabatic evolution. We evaluate these geometric phases using Floquet theory for systems in time-dependent external fields with a focus on paths leading through a degeneracy of the eigenenergies. Contrary to expectations, the low-frequency limits of the two phases do not always coincide. This happens as the degeneracy leads to a slow convergence of the quantum states to adiabaticity, resulting in a nonzero finite or divergent contribution to the AA phase. Steering the system adiabatically through a degeneracy provides control over the geometric phase as it can cause a π shift of the Berry phase. On the other hand, we revisit an example of degeneracy crossing proposed by AA. We find that, at suitable driving frequencies, both geometric-phase definitions give the same result and the dynamical phase is zero due to the symmetry of time evolution about the point of degeneracy, providing an advantageous setup for manipulation of quantum states.

Constraining the orbital eccentricity of inspiralling compact binary systems with Advanced LIGO

The detection of ~50 coalescing compact binaries with the Advanced LIGO and Virgo detectors has allowed us to test general relativity, constrain merger rates, and look for evidence of tidal effects, compact object spins, higher waveform modes, and black hole ringdowns. An effect that has not yet been confidently detected is binary eccentricity, which might be present in a small fraction of binaries formed dynamically. Here we discuss general limits on eccentricity that can, in-principle, be placed on all types of compact object binaries by a detector operating at the design sensitivity of Advanced LIGO. Using a post-Newtonian model for gravitational-wave phasing valid in the small eccentricity regime, we assess the relative measurement error for eccentricity for a variety of spinning and non-spinning binaries. Errors and correlations involving the mass and spin parameters are also investigated. We find that decreasing the low frequency limit of a detector's observational frequency band is one of the key design factors for increasing the odds of measuring binary eccentricity. We also introduce and analytically explore the eccentric chirp mass parameter, which replaces the chirp mass as the key measurable parameter combination in eccentric gravitational waveform models. The eccentric chirp mass parameter explains a degeneracy between the chirp mass and the eccentricity. This degeneracy leads to a bias in the standard chirp mass parameter. We also investigate the systematic parameter bias that arises when eccentric systems are recovered using circular waveform templates. We use both Fisher matrix and Bayesian-inference-based Markov Chain Monte Carlo (MCMC) methods to investigate these parameter estimation issues, and we find good agreement between the two approaches (for both statistical and systematic errors) in the appropriate signal-to-noise ratio regime. (abridged)

Fundamental Limits on Substructure Dielectric Resonator Antennas

We show theoretically that the characteristic modes of dielectric resonator antennas (DRAs) must be capacitive in the low frequency limit and that as a consequence of this constraint and the Poincaré Separation Theorem, the modes of any DRA consisting of partial elements of an encompassing super-structure with the same spatial material properties cannot resonate at a lower frequency than the encompassing structure. Thus, design techniques relying on complex sub-structures to miniaturize the antenna, including topology optimization and meandered windings, cannot apply to DRAs. Due to the capacitive nature of the DRA modes, it is also shown that the Q factor of any DRA sub-structure will be bounded from below by that of the super-structure at frequencies below the first self-resonance of the super-structure. We demonstrate these bounding relations with numerical examples.

Density of States Effects on Emission and Scattering of Photons in Plasmas

Plasma supports electromagnetic waves propagation for frequencies higher than plasma frequency but features dielectric permittivity less than 1. This property leads to photon density of states (DOS) lower than in vacuum and should result in subnatural spectral linewidths, sub-Planckian spectrum of thermal radiation, and in sub-Rayleigh photon scattering as well as in lower inelastic photon scattering including Raman scattering in molecular and crystalline structures. We emphasize the basic character of these phenomena though absolute values of corrections from this property of plasmas in many real experiments may appear to be small as compared to other factors. We found that dissipative losses when being taken into account make possible DOS effects smaller though not vanishing and additionally bring about indefinite growth of DOS in the low-frequency limit.

High sensitivity and broad detection range flexible capacitive pressure sensor based on rGO cotton fiber for human motion detection

Recently, flexible pressure sensors have attracted considerable interest in electronic skins, wearable devices, intelligent robots and biomedical diagnostics. However, the design of high sensitivity flexible pressure sensors often relies on expensive materials and complex process technology, which greatly limit their popularity and applications. Even worse, chemical-based sensors are poorly biocompatible and harmful to the environment. Here, we developed a flexible capacitive pressure sensor based on reduced graphene oxide cotton fiber by a simple and low-cost preparation process. The environmentally friendly sensor exhibited a comprehensive performance with not only ultra-high sensitivity (up to 15.84 kPa−1) and a broad sensing range (0–500 kPa), but also excellent repeatability (over 400 cycles), low hysteresis (⩽11.6%), low detection limit (<0.1 kPa) and wide frequency availability (sensitivity from 19.71 to 11.24 kPa−1, frequency from 100 Hz to 10 kHz). Based on its superior performance, the proposed sensor can detect various external stimuli (vertical stress, bending and airflow) and has been successfully applied for facial expression recognition, breathing detection, joint movement and walking detection, showing great potential for application in artificial electronic skin and wearable healthcare devices.

Growth of vortical disturbances entrained in the entrance region of a circular pipe

The development and growth of unsteady three-dimensional vortical disturbances entrained in the entry region of a circular pipe is investigated by asymptotic and numerical methods for Reynolds numbers between $1000$ and $10\,000$ , based on the pipe radius and the bulk velocity. Near the pipe mouth, composite asymptotic solutions describe the dynamics of the oncoming disturbances, revealing how these disturbances are altered by the viscous layer attached to the pipe wall. The perturbation velocity profiles near the pipe mouth are employed as rigorous initial conditions for the boundary-region equations, which describe the flow in the limit of low frequency and large Reynolds number. The disturbance flow is initially primarily present within the base-flow boundary layer in the form of streamwise-elongated vortical structures, i.e. the streamwise velocity component displays an intense algebraic growth, while the cross-flow velocity components decay. Farther downstream the disturbance flow occupies the whole pipe, although the base flow is mostly inviscid in the core. The transient growth and subsequent viscous decay are confined in the entrance region, i.e. where the base flow has not reached the fully developed Poiseuille profile. Increasing the Reynolds number and decreasing the frequency causes more intense perturbations, whereas small azimuthal wavelengths and radial characteristic length scales intensify the viscous dissipation of the disturbance. The azimuthal wavelength that causes the maximum growth is found. The velocity profiles are compared successfully with available experimental data and the theoretical results are helpful to interpret the only direct numerical dataset of a disturbed pipe-entry flow.

Scalar absorption cross section of rotating black holes with tidal charge

The absorption cross section of rotating black holes in the Randall-Sundrum brane-world scenario for massless scalar waves is obtained via the partial-wave method. A variety of incidence directions with respect to the black hole rotation axis is considered. Special attention is given to near-extreme black holes, in which cases the absorption cross section increases as the tidal charge becomes more negative. It is shown that black holes with different configurations can present capture cross sections/shadows of same size. However, in such cases, the absorption spectra are different mainly for small frequencies. Numeric results are compared with the capture cross sections in the high-frequency limit, and with the black hole area in the low-frequency limit showing good agreement.

Quantum gates robust to secular amplitude drifts

Quantum gates are typically vulnerable to imperfections in the classical control fields applied to physical qubits to drive the gates. One approach to reduce this source of error is to break the gate into parts, known as composite pulses (CPs), that typically leverage the constancy of the error over time to mitigate its impact on gate fidelity. Here we extend this technique to suppress secular drifts in Rabi frequency by regarding them as sums of power-law drifts whose first-order effects on over- or under-rotation of the state vector add linearly. Power-law drifts have the form $t^p$ where $t$ is time and the constant $p$ is its power. We show that composite pulses that suppress all power-law drifts with $p \leq n$ are also high-pass filters of filter order $n+1$ arXiv:1410.1624. We present sequences that satisfy our proposed power-law amplitude criteria, $\text{PLA}(n)$, obtained with this technique, and compare their simulated performance under time-dependent amplitude errors to some traditional composite pulse sequences. We find that there is a range of noise frequencies for which the $\text{PLA}(n)$ sequences provide more error suppression than the traditional sequences, but in the low frequency limit, non-linear effects become more important for gate fidelity than frequency roll-off. As a result, the previously known $F_1$ sequence, which is one of the two solutions to the $\text{PLA}(1)$ criteria and furnishes suppression of both linear secular drift and the first order nonlinear effects, is a sharper noise filter than any of the other $\text{PLA}(n)$ sequences in the low frequency limit.

Microwave response of an Andreev bound state

We develop a theory for the dynamics of an Andreev bound state hosted by a weak link of finite length for which charging effects are important. We derive the linear response of both the current through the link and charge accumulated in it with respect to the phase and gate voltage biases. The resulting matrix encapsulates the spectroscopic properties of a weak link embedded in a microwave resonator. In the low-frequency limit, we obtain the response functions analytically using an effective low-energy Hamiltonian, which we derive. This Hamiltonian minimally accounts for Coulomb interaction and is suitable for a phenomenological description of a weak link having a finite length.

Energy spreading, equipartition, and chaos in lattices with non-central forces

We numerically study a one-dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one-dimensional mass-spring system, the linear dispersion relation of the considered model has different characteristics in the low frequency limit. By introducing disorder in the masses of the lattice particles, we investigate how different nonlinearities in the potential (cubic, quadratic, and their combination) lead to energy delocalization, equipartition, and chaotic dynamics. We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation. Beyond a certain energy threshold, when the cubic nonlinearity is present, the system is found to reach energy equipartition and total delocalization. On the other hand, when only the quartic nonlinearity is activated, the system remains localized and away from equipartition at least for the energies and evolution times considered here. However, for large enough energies for all types of nonlinearities we observe chaos. This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present, while the appearance of only quadratic nonlinearity leads to energy localization. Our results reveal a rich dynamical behavior and show differences with the relevant Fermi–Pasta–Ulam–Tsingou model. Our findings pave the way for the study of models relevant to bending (flexural) waves in the presence of nonlinearity and disorder, anticipating different energy transport behaviors.

From Quantum Rabi Model To Jaynes–Cummings Model: Symmetry‐Breaking Quantum Phase Transitions, Symmetry‐Protected Topological Transitions and Multicriticality

AbstractThe ground state and excitation gap are studied for the anisotropic quantum Rabi model (QRM) which connects the fundamental QRM and the Jaynes–Cummings model (JCM). While conventionally the ground state has a second‐order quantum phase transition in the low frequency limit, turning on finite frequencies sheds a novel light on the phase diagram to illuminate a fine structure of first‐order transition series. It is found that the conventional quantum phase transition is accompanied with a hidden symmetry breaking, whereas the emerging series transitions are topological transitions without symmetry breaking. The topological structure of the wave function provides a novel universality classification in bridging the QRM and the JCM among the diversity that arises from finite frequencies. The aspect of topological transitions provides a renewed insight for the role of the counter‐rotating interaction. Moreover, it is shown that the conventionally established tricritical point is actually a pentacritical or hexacritical point and following this multicritical point emerges a series of quadruple points. Besides the emerging multicriticality and reformed universality, the result demonstrates that a single‐qubit system can even exhibit analogs of topological phase transitions which traditionally occur in condensed matter.

Searching for High-z Radio Galaxies with the MGCLS

We present the results from a search for high-redshift radio galaxy (HzRG) candidates using 1.28 GHz data in the Abell 2751 field drawn from the MeerKAT Galaxy Cluster Legacy Survey (MGCLS). We used the HzRG criteria that a radio source is undetected in all-sky optical and infrared catalogues and that it has a very steep radio spectrum. We used the likelihood ratio method for cross-matching the radio catalogue against multi-wavelength galaxy catalogues from the Dark Energy Camera Legacy Survey (DECaLS) and the All-sky Wide Infrared Survey Explorer (AllWISE). For those radio sources with no multi-wavelength counterpart, we further implemented a radio spectral index criterium of α&lt;−1, using in-band spectral index measurements from the wide-band MeerKAT data. Using a 5σ signal-to-noise cut on the radio flux densities, we found a total of 274 HzRG candidates: 179 ultra-steep spectrum sources and 95 potential candidates, which could not be ruled out as they had no spectral information available. The spectral index assignments in this work were complete above a flux density of 0.3 mJy, which is at least an order of magnitude lower than existing studies in this frequency range or when extrapolating from lower frequency limits. Our faintest HzRG candidates with and without an in-band spectral index measurement had a 1.28 GHz flux density of 57 ± 8 μJy and 68 ± 13 μJy, respectively. Although our study is not complete down to these flux densities, our results indicate that the sensitivity and bandwidth of the MGCLS data make them a powerful radio resource to search for HzRG candidates in the Southern sky, with 20 of the MGCLS pointings having similar image quality as the Abell 2751 field and full coverage in both DECaLS and AllWISE. Data at additional radio frequencies will be needed for the faintest source populations, which could be provided in the near future by the MeerKAT UHF band (580–1015 MHz) at a similar resolution (∼8–10″).

Thermodynamics and transport of holographic nodal line semimetals

We study various thermodynamic and transport properties of a holographic model of a nodal line semimetal (NLSM) at finite temperature, including the quantum phase transition to a topologically trivial phase, with Dirac semimetal-like conductivity. At zero temperature, composite fermion spectral functions obtained from holography are known to exhibit multiple Fermi surfaces. Similarly, for the holographic NLSM we observe multiple nodal lines instead of just one. We show, however, that as the temperature is raised these nodal lines broaden and disappear into the continuum one by one, so there is a finite range of temperatures for which there is only a single nodal line visible in the spectrum. We compute several transport coefficients in the holographic NLSM as a function of temperature, namely the charge and thermal conductivities, and the shear viscosities. By adding a new non-linear coupling to the model we are able to control the low frequency limit of the electrical conductivity in the direction orthogonal to the plane of the nodal line, allowing us to better match the conductivity of real NLSMs. The boundary quantum field theory is anisotropic and therefore has explicitly broken Lorentz invariance, which leads to a stress tensor that is not symmetric. This has important consequences for the energy and momentum transport: the thermal conductivity at vanishing charge density is not simply fixed by a Ward identity, and there are a much larger number of independent shear viscosities than in a Lorentz-invariant system.

A Non-Compact Effective Impedance Model for Can-to-Can Acoustic Communication: Analysis and Optimization of Damping Mechanisms

Abstract Can-annular combustors can feature azimuthal instabilities even if the acoustic coupling between the individual cans is weak. Recently, various studies have focused on modeling the acoustic communication between adjacent cans in can-annular systems. In this study, a coupling model is presented that, in contrast to previous models, includes the effect of density fluctuations, mean flow, and dissipative effects at the connection gaps. By assuming plane acoustic waves inside each can and exploiting the discrete rotational symmetry of the can-annular system, the acoustic can-to-can interaction can be represented by an effective Bloch-type impedance. A single can modeled with the effective impedance at the downstream end emulates the acoustic response of the entire can-annular arrangement. We then propose the idea of installing a liner just upstream of the first turbine stage to damp azimuthal instabilities. By using the proposed can-to-can coupling model, we discuss in detail the effect that the impedance of the liner has on the effective reflection coefficient for different Bloch wavenumbers. In the low-frequency limit, we derive an analytical condition for achieving maximum damping at a specific Bloch-number. We show that the damping of azimuthal modes depends on the porosity of the liner, mean flow parameters and the Bloch-structure of the mode. These results suggest the possibility of targeting the damping of modes of certain azimuthal order by geometric variations of the liner or of the connection gap. As an exemplary application of the theory, we setup a network model of a generic industrial 12-can combustor and investigate a cluster of acoustic and thermoacoustic eigenvalues for a varying liner porosity. The findings of this study provide a deeper understanding of the mechanisms that drive the can-to-can acoustic communication, and open the path for devising passive damping strategies aimed at stabilizing specific modes in can-annular combustors.

Influence of activation energy on charge conduction mechanism and giant dielectric relaxation of sol-gel derived C3H7NH3PbBr3 perovskite; Act as high performing UV photodetector

This work contains an extensive study on temperature dependent complex dielectric behavior over 4 Hz≤ f≤ 8 MHz of a promising hybrid perovskite, propylammonium lead bromide. The structural, as well as morphological property of this sol-gel derived sample have been analyzed with the help of XRD and SEM respectively. The obtained energy band gap and thermal stability study ensure the capability of this material in device fabrication. Possessing a wide band gap, this perovskite fascinatingly serves as a UV photodetector. The individual impact of grain and grain boundary over the entire resistance has been resolved by Maxwell – Wagner Cole–Cole model. This material holds an amazing property; giant dielectric constant near room temperature at low frequency limit which escalates rapidly in the influence of thermal effect. Modified cole – cole plot assures that both space and free charge conductivities ascend with temperature. The asymmetrical nature of the imaginary part of electric modulus is analyzed by Kohlrausch – Williams – Watts which confirms its non – Debye nature diminishes with rising temperature. The thermally triggered AC conductivity follows Jonscher’s power law and is emphasized with the jump relaxation model. The bulk conductivity of the sample depends on temperature and is elucidated with variable range hopping of localized charge carriers. Activation energy plays a key role in the ionic conduction mechanism within the sample, described elaborately. The overall substantial studies on its application as UV detector and different dielectric properties of this sample construct the basis of appreciable acceptability of the sample in energy harvesting.

Theory for attenuation and dispersion of acoustic propagation through a muddy medium

Mud as a medium typically consists of clay particles, small silt particles (primarily quartz), and water. The clay particles lock together in what is called a card-house configuration, and the silt particles are held in suspension by the card house. The low frequency velocity of sound waves appears to be well-predicted by the Mallock-Wood theory that gives weighted averages of bulk compressibility and material density. At low frequencies, the attenuation is caused by the viscous dag of the water on the suspended silt particles, and the attenuation varies as the frequency squared. The deviation of the phase velocity from the low frequency limit at low frequencies is less well-understood but appears to vary as the frequency to the three-halfs. At higher frequencies, the dominant mechanism appears to be a relaxation mechanism associated with the card house. Each clay particle carries a net electrical charge and the resulting repulsion forces the clay particles to be spatially separated. However, the particles tend to stick together edge to face, and the van der Waals attraction between the clay particles tends to dominate over the electrostatic repulsion. However, the passage of a sound wave temporarily breaks some van der Waals bonds and they subsequently recombine as the acoustic pressure ebbs. The present paper seeks to quantify the effects of the relaxation processes. It is demonstrated that the latter leads to an attenuation that, at higher frequencies, varies nearly linearly with frequency. [Work supported by ONR.]

Odd-frequency pairing inherent in a Bogoliubov Fermi liquid

The disorder and interaction effects on Bogoliubov-Fermi surfaces with preserved inversion symmetry are studied for a low-energy effective model coupled to bosonic degrees of freedom. It is shown that the non-ideal Bogoliubov quasiparticles (bogolons) generically induce the odd-frequency pair amplitude which reflects a Cooper pairing at different time. The self-energy of bogolons is mainly contributed by the disorder effects in the low frequency limit as in the usual electron liquid. Depending on the choice of the parameters, there are two kinds of solutions: one is frequency-independent (but with sign function of frequency) and the other is proportional to the inverse of the frequency, which exist in both the normal and anomalous parts of the self-energy. These characteristic self-energy structures are clearly reflected in the single-particle spectrum. Since the bogolons are originally composed of electrons, the connection between the two is also sought using the concrete $j=3/2$ fermion model, which reveals that the odd-frequency pairing of bogolons is mainly made of the electrons' odd-frequency pairing.

Python-based reduced order quadrature building code for fast gravitational wave inference

The next generation of gravitational wave observatories will reach low frequency limits on the orders of a few Hz, thus enabling the detection of gravitational wave signals of very long duration. The run time of standard parameter estimation techniques with these long waveforms can be months or even years, making it impractical with existing Bayesian inference pipelines. Reduced order modeling and the reduced order quadrature integration rule have recently been exploited as promising techniques that can greatly reduce parameter estimation computational costs. We describe a Python-based reduced order quadrature building code, pyroq, which builds the reduced order quadrature data needed to accelerate parameter estimation of gravitational waves. We present the first bases for the imrphenomxphm waveform model of binary-black-hole coalescences, including subdominant harmonic modes and precessing spins effects.

Effective medium theory for photonic crystals with quadrupole resonances.

An effective medium theory is proposed to characterize two-dimensional dielectric photonic crystals (PCs) exhibiting quadrupole resonances. In addition to the effective permittivity and permeability associated with electric and magnetic dipoles, we obtain a local effective parameter to describe the contributions of quadrupole resonances by taking the low frequency limit of multiple-scattering theory. These effective parameters can be used to predict the characteristics of double-Dirac-cone PCs, showing good agreement with the numerical results. Moreover, we show that, after introducing the new effective parameter, the double-Dirac-cone PCs can be regarded as a generalization of the traditional double-zero-index metamaterials.